Diagonally Stable Tridiagonal Switched Linear Systems
نویسنده
چکیده
Abstract: A stability analysis is carried out for certain classes of switched linear systems with tridiagonal structure, under arbitrary switching signal. This analysis is made using diagonal common quadratic Lyapunov functions. Namely, necessary and sufficient conditions for the existence of such Lyapunov functions are proposed for second order switched systems and for third order switched systems with Toeplitz tridiagonal structure.
منابع مشابه
Mathematical Modeling and Analysis An Efficient, Numerically Stable, and Scalable Parallel Tridiagonal Solver
We describe a stable, efficient, parallel algorithm for the solution of diagonally dominant tridiagonal linear systems that scales well on distributed memory parallel computers. This algorithm is in the class of partitioning algorithms. Its multi-level recursive design makes it well suited for distributed memory parallel computers with very large numbers of processors. The need to solve large t...
متن کاملIncomplete Cyclic Reduction of Banded and Strictly Diagonally Dominant Linear Systems
The ScaLAPACK library contains a pair of routines for solving banded linear systems which are strictly diagonally dominant by rows. Mathematically, the algorithm is complete block cyclic reduction corresponding to a particular block partitioning of the system. In this paper we extend Heller’s analysis of incomplete cyclic reduction for block tridiagonal systems to the ScaLAPACK case. We obtain ...
متن کاملA Memory Efficient Parallel Tridiagonal Solver
We present a memory efficient parallel algorithm for the solution of tridiagonal linear systems of equations that are diagonally dominant on a very large number of processors. Our algorithm can be viewed as a parallel partitioning algorithm. We illustrate its performance using some examples. Based on this partitioning algorithm, we introduce a recursive version that has logarithmic communicatio...
متن کاملAn Analysis of the Parallel Computation of Arbitrarily Branched Cable Neuron Models
We present and analyze a parallel method for the solution of partial diierential equation models of the nervous system. These models mathematically are one-dimensional nonlinear parabolic equations deened on branching domains. Implicit methods for these equations leads to numerical solution of diagonally dominant almost tridiagonal linear systems at each time step. We rst review some exact meth...
متن کاملA Comparison of Parallel Solvers for Diagonally Dominant and General Narrow-Banded Linear Systems
We investigate and compare stable parallel algorithms for solving diagonally dominant and general narrow-banded linear systems of equations. Narrow-banded means that the bandwidth is very small compared with the matrix order and is typically between 1 and 100. The solvers compared are the banded system solvers of ScaLAPACK [11] and those investigated by Arbenz and Hegland [3, 6]. For the diagon...
متن کامل